Question

Kinda urgent math question?
Does a higher interquartile range mean more consistency?

Answer 1

I have to disagree with the first poster. The size of the interquartile range should *not* be a measure of the sample size. I seem to remember that it's an unbiased estimator.

The interquartile range is a measure of the "central tendency" just like the standard deviation. Half the data points lie within the interquartile range (and that's true whether you have 20 measurements or 10,000). A small interquartile range means that the data are very consistent (most values lie close to each other).

The advantage of the interquartile range over the standard deviation is that the interquartile range includes half the data points regardless of the shape of the distribution. The most common uses of the standard deviation, on the other hand, require that you assume a normal distribution.

The median is the number in the middle of the distribution. Half the data points lie above it, and half lie below it. For a symmetrical distribution, the median will lie halfway between the first quartile and the third quartile -- if it isn't, you know that the distribution is not symmetrical (skewed).

The median is useful because it isn't influenced by extreme values. You might collect 20 people and ask them their income, because you wanted to know how much money people usually make. If Bill Gates walked into the room, the average would be pretty meaningless, but the median would still answer your question.

Answer 2

wow. this is pretty helpful. But may I ask what they would mean by a 'higher' interquartile range? And how it might be (even though you may disagree) related to consistency?

Answer 3

The inter-quartile range is a measure that indicates the extent to which the central 50% of values within the dataset are dispersed. It is based upon, and related to, the median.

In the same way that the median divides a dataset into two halves, it can be further divided into quarters by identifying the upper and lower quartiles. The lower quartile is found one quarter of the way along a dataset when the values have been arranged in order of magnitude; the upper quartile is found three quarters along the dataset. Therefore, the upper quartile lies half way between the median and the highest value in the dataset whilst the lower quartile lies halfway between the median and the lowest value in the dataset. The inter-quartile range is found by subtracting the lower quartile from the upper quartile.

For example, the examination marks for 20 students following a particular module are arranged in order of magnitude.

Answer 4

It still doesn't answer my question about consistency though (how do you even type so fast)

Answer 5

here http://www2.le.ac.uk/offices/ld/resources/numerical-data/variability

Answer 6

because hes copying and pasting...lol

Answer 7

And here I thought there was a record breaker for fastest typer

Answer 8

But does anyone know anything about relation between this interquartile range and consistency?

Answer 9

it is ,however, correct

Answer 10

what is correct?

Answer 11

The interquartile range is the upper quartile (75th percentile) minus (-) the lower percentile (75th percentile). The interquartile range uses 50% of the data. It is a measure of the "central tendency" just like the standard deviation.<br />A small interquartile range means that most of the values lie close to each other.

Answer 12

smaller IQR's are more consistent because the numbers are closer together

Answer 13

Ahhhhhh THANKS GUYS :D

Answer 14

np